Methods of making a rolling bearing race provided with a continuous rupture seam along at least one area of its periphery and having a seating surface and a race surface for rolling elements, the rolling seating race surface being exposed before rupture along at least a part of the intended course of the rupture seam to high-energy radiation which radiates transversely within local confines to the intended course of the rupture seam, and, during rupture, the area of the surface exposed to radiation is subjected to tensile load by an external force are known and are used for hardened rolling bearing races. These methods are based on the penetration of high-energy radiation to create locally within the texture of the rolling bearing race an extreme brittleness acting as a quasi "inner groove" along which the rolling bearing race is split by the influence of an external force which is especially small when acting on the rolling bearing race so that the area of its surface exposed to radiation is subjected to tensile load. Such a method is known (DE-OS No. 3,425,829, FIG. 1) and has been proven commercially. However, the occasional chipping off of material from the running surface during rupture along the rupture seam so that the respective bearing race became useless is a disadvantage thereof.